First principles simulations of nanomaterials for nanoelectronics and spintronics

2 1.2 Molecular electronic devices: molecular diode and molecular switch 4 1.2.1 Molecular diode.. 51 4 Functionalization of gold nanotubes and carbon nanotubes 54 4.1 Adsorbate and defe

First-principles Simulations of Nanomaterials for

Nanoelectronics and Spintronics

CAI YONGQING

(B.Sc., Northwestern Polytechnical University)

A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF PHYSICS NATIONAL UNIVERSITY OF SINGAPORE

2011

I would like to thank my co-supervisor Dr Zhang Chun, who has provided a lot

of help and suggestions on my research work I got many insights from discussionswith his sharp mind and plenty of experience in the computational physics

I would like to thank the previous and current members in the group At the earlystage of my research, I got a lot of help from Wu Rongqin, Peng Guowen, and

Lu Yunhao I had many useful discussions with them and other group membersincluding Ge MinYuan, Yang Ming, Zhou Miao, Sha Zhendong, Shen Lei, BaiZhaoqiang, Dai Zhenxiang, Zhang Aihua, and Yang Kesong

At last, I would like to thank my parents, relatives and friends Especially i thank

my parents for their support and love, and thanks Ke Qingqing for being patientand enlightening with me in the past three years

Table of Contents

1.1 Quasi one-dimensional (1D) nanomaterials as building blocks of

na-noelectronics 2

1.2 Molecular electronic devices: molecular diode and molecular switch 4 1.2.1 Molecular diode 4

1.2.2 Molecular switch 6

1.3 Highly spin-polarized materials for spintronics 9

1.4 Objectives and scope of the thesis 12

2 First-principles Methods 15 2.1 Density functional theory 16

2.1.1 Hohenberg-Kohn theory and Kohn-Sham equation 17

2.1.2 LDA and GGA 20

2.2 Implementation of density functional theory 22

2.2.1 Pseudopotential 22

2.2.2 Planewave Basis 25

2.3 Non-equilibrium Green’s function method 26

2.3.1 Green’s function 26

2.3.2 Open systems and NEGF 28

2.3.3 Implementation of NEGF combined with DFT 30

3 Switching and rectification of a single light-sensitive diarylethene molecule sandwiched between graphene nanoribbons 33 3.1 Computational details 35

3.2 Photochromic switching 37

3.2.1 Molecular electronic structure 37

3.2.2 Linear conductance and molecular switch 38

3.3 Rectification 44

3.4 Summary 51

4 Functionalization of gold nanotubes and carbon nanotubes 54 4.1 Adsorbate and defect effects on electronic and transport properties of gold nanotubes 55

4.1.1 Computational details 55

4.1.2 Structures and energetics of adsorbates on gold nanotubes 55 4.1.3 Electronic structures of CO and O adsorbed gold nanotubes 60 4.1.4 Conductance of CO and O absorbed Au tubes 64

4.1.5 Defect effects on conductance of Au tubes: Au adsorbate

and vacancy 66

4.2 Mechanically and chemically tuning of the work function of CNT 68 4.2.1 Work function of CNT 68

4.2.2 Computational details 69

4.2.3 Strain effects on work function of pristine CNT 71

4.2.4 Work function of potassium-adsorbed CNT 74

4.2.5 Strain effect on work function of potassium-decorated CNT 75 4.3 Summary 79

5 Strain effect on the spin injection and electronic tunneling of Co2CrAl/NaNbO3/Co2CrAl 82 5.1 Computational details 83

5.2 Energetics and electronic structure analysis 84

5.3 Strain effects on the spin injection and tunnel magnetoresistance 88

5.4 Strain effects on the tunnel magnetoresistance 91

5.5 Summary 94

6 Conclusions and perspectives 95

Rapid developments of nanoelectronics and spintronics call for the design of newmaterials for building blocks of nanoscale electronic devices In this thesis, firstprinciples calculations were carried out to study the physical properties of variouskinds of nanomaterials and investigate their potential applications in nanoelectron-ics and spintronics

Firstly, we studied coherent electronic transport through a single light sensitive arylethene molecule sandwiched between two graphene nanoribbons (GNRs) The

di-“open” and “closed” isomers of the diarylethene molecule that can be convertedbetween each other upon photo-excitation were found to have drastically differ-ent current-voltage characteristics More importantly, when one GNR is metallicand another one is semiconducting, strong rectification behavior of the “closed”

diarylethene isomer with the rectification ratio >103 was observed The resultsopen possibilities for the design of a new class of molecular electronic devices

Secondly, electronic and/or transport properties of gold nanotubes and carbonnanotubes (CNTs) were studied For gold nanotubes, effects of adsorbates (COmolecule and O atom) and defects on the electronic and transport properties of

Au (5,3) and Au (5,5) nanotubes were investigated After CO adsorption, the

conductance of Au (5,3) decreases by 0.9 G0, and the conductance of Au (5,5)

decreases by approximately 0.5 G0 For O adsorbed Au tubes, O atoms strongly

interact with Au tubes, leading to around 2 G0 of drop of conductance for both

Au tubes When a monovacancy defect is present, the conductance decreases by

around 1 G0 for both tubes For CNT, strain dependence of work functions of bothpristine and potassium doped CNTs was calculated We found that for pristinecases, the uniaxial strain has strong effects on the work functions of CNTs, andthe responses of work functions of CNT (5,5) and (9,0) to the strain are distinctlydifferent When coated with potassium, for both CNTs, work functions can bereduced by more than 2.0 eV, and the strain dependence of work functions changesdrastically

Finally, effects of strain on transport properties of Co2CrAl/NaNbO3/Co2CrAlmagnetic tunneling junction (MTJ) were studied Both spin polarization and tun-nel magnetoresistance (TMR) of the MTJ were found to respond to positive (ten-sile) and negative (compressive) strains asymmetrically While a compressive strain

up to 4% causes slight increases in the spin polarization and small fluctuations inTMR, a tensile strain of a few percent significantly reduces the TMR This studyprovides a theoretical understanding on relationship between transport propertiesthrough a MTJ and interface atomic structural changes induced by an externalstrain

[1] Yongqing Cai, Miao Zhou, Minggang Zeng, Chun Zhang, Yuan Ping Feng, sorbate and defect effects on electronic and transport properties of gold nanotubes”,Nanotechnology 22, 215702 (2011)

“Ad-[2] Yongqing Cai, Aihua Zhang, Yuan Ping Feng, Chun Zhang, Hao Fatt Teoh,Ghim Wei Ho, “Strain effects on work functions of pristine and potassium-decoratedcarbon nanotubes”, J Chem Phys., 131, 224701 (2009)

[3] M G Zeng, L Shen, Y Q Cai, Z D Sha, Y P Feng, “Perfect spin-filter andspin-valve in carbon atomic chains”, Appl Phys Lett 96, 042104 (2010)

[4] M Zhou, Y Q Cai, M G Zeng, C Zhang, Y P Feng, “Mn-doped thiolatedAu-25 nanoclusters: Atomic configuration, magnetic properties, and a possiblehigh-performance spin filter”, Appl Phys Lett 98, 143103 (2011)

[5] Yongqing Cai, Chun Zhang, Yuan Ping Feng, “Dielectric properties and lattice

dynamics of α-PbO2-type TiO2: The role of soft phonon modes in pressure-inducedphase transition to baddeleyite-type TiO2”, Phys Rev B 84, 094107 (2011)

[6] Yongqing Cai, et al., “Strain effect on the spin injection and electronic ductance of Co2CrAl/NaNbO3/Co2CrAl magnetic tunneling junction”, Manuscript

con-finished for Phys Rev B submission.

[7] Yongqing Cai, Aihua Zhang, Yuan Ping Feng, and Chun Zhang, “Switching

and Rectification of a Single Light-sensitive Diarylethene Molecule Sandwiched

between Graphene Nanoribbons”, J Chem Phys 135, 184703 (2011)

[8] Y H Lu, R Q Wu, L Shen, M Yang, Z D Sha, Y Q Cai, P M He, Y P

Feng, “Effects of edge passivation by hydrogen on electronic structure of armchair

graphene nanoribbon and band gap engineering”, Appl Phys Lett 94, 122111

(2009)

[9] Z D Sha, R Q Wu, Y H Lu, L Shen, M Yang, Y Q Cai, Y P Feng, Y

Li, “Glass forming abilities of binary Cu(100-x)Zr(x) (34, 35.5, and 38.2 at %)

metallic glasses: A LAMMPS study”, J Appl Phys 105, 043521 (2009)

[10] M Yang, R Q Wu, W S Deng, L Shen, Z D Sha, Y Q Cai, Y P Feng, J

S Wang, “Electronic structures of beta-Si(3)N(4)(0001)/Si(111) interfaces: Perfect

bonding and dangling bond effects”, J Appl Phys 105, 024108 (2009)

[11] R Q Wu, L Shen, M Yang, Z D Sha, Y Q Cai, Y P Feng, Z G Huang,

Q Y Wu, “Enhancing hole concentration in AlN by Mg : O codoping: Ab initio

study”, Phys Rev B 77, 073203 (2008)

[12] R Q Wu, L Shen, M Yang, Z D Sha, Y Q Cai, Y P Feng, Z G Huang,

Q Y Wu, “Possible efficient p-type doping of AlN using Be: An ab initio study”,

Appl Phys Lett 91, 152110 (2007)

[13] Zhaoqiang Bai, Yongqing Cai, Lei Shen, Ming Yang, Viloane Ko, Guchang

Han, and Yuanping Feng, Magnetic and transport properties of Mn3−xGa/MgO/Mn3−xGa

magnetic tunnel junctions: A first-principles study, Appl Phys Lett 100, 022408(2012).

List of Tables

4.1 Energetics and structures of adsorbates (CO, O, Au) on Au (5,3)

and Au (5,5) nanotubes d is the shortest length of the bonds formed

by Au and adsorbates; δQ x (x =CO, O, Au) and δQ Au are the netpartial charge transfers of the adsorbates and the Au atom with theshortest distance from the adsorbates 58

5.1 Calculated cohesive energies and interface bond lengths for variousCCA/NNO interfaces 86

List of Figures

1.1 A molecular switch based on tuning the molecular orbital with tric field Reprinted with permission from Ref.[56] 7

elec-1.2 Switching cycle of diarylethenes 8

1.3 Schematic pictures of density of states (DOS) of paramagnet, magnet, and half metal 12

ferro-2.1 Schematic illustration of the replacement of the all-electron function and core potential by a pseudo-wavefunction and pseudopo-tential 24

wave-3.1 Molecular structures and photochemical interconversion of the “closed”and “open” diarylethene The molecule can be divided into core,spacer, and linker groups 34

3.2 (a) Supercells of optimized 6-zGNR-“closed” diarylethene-6-zGNRand 14-aGNR-“open” diarylethene-14-aGNR junctions Red, blue,violet and yellow lines denote bonds formed by O, N, C and S, re-spectively Note that hydrogen atoms are not shown in the figure.The shadowed area denotes portions in the supercell chosen as elec-trodes (b) Band structures of 10-, 12-, and 14-aGNR and 6-zGNR.The calculated band gaps are 1.21, 0.54, 0.22 eV for 10-aGNR, 12-aGNR and 14-aGNR respectively Ca and Cz are the lattice constant

of the unit cell of the aGNR and zGNR, respectively 36

3.3 Lineup of orbitals for “open” (left) and “closed” (right) diarylethene 38

3.4 Conductance spectra at zero bias of 6-zGNR-diarylethene-6-zGNR(a) and 14-aGNR-diarylethene-14-aGNR (b) junctions with “closed”(blue) and “open” (red) isomers The short lines above the plotsshow the HOMO/LUMO alignments with the electrode Fermi level.(c) Isosurface plot of transmission eigenstates at EF for “closed”(left) and “open” (right) isomers of diarylethene with 6-zGNR elec-trodes 39

3.5 I-V characteristics of (a) aGNRs and (b) 6-zGNR diarylethene

junc-tions 40

3.6 Variation of logarithmic transmission curves with voltage logT(e,V)

for (a)10-aGNR, (b)12-aGNR, (c)14-aGNR and (d) 6-zGNR metrical junctions with diarylethene in the “closed” form Evolu-tions of HOMO-2 and HOMO-3 of the “closed” molecule as a func-tion of voltage are shown by white points; 42

sym-3.7 Mulliken charge analysis for the “closed” diarylethene molecule bedded in symmetric GNRs junctions 44

em-3.8 (a) Optimized atomic configuration of the 6-zGNR-diarylethene 10-aGNR junction (b) Evolution of MPSH levels as a function

(“closed”)-of voltage for the 6-zGNR-diarylethene-10-aGNR junction with the

“closed” diarylethene Blue dotted lines indicate Fermi energy els of two electrodes The shadowed area depicts the movement of

lev-the band gap of 10-aGNR under biases (c) I-V characteristics of 6-zGNR-(“closed”) diarylethene-x -aGNR (x =10, 12 and 14) junc-

tions The inset shows the rectification ratio (RR) of these junctionsfrom 0.4 to 1.0 V 46

3.9 Variation of logarithmic transmission curves with voltage logT(e,V)

for asymmetrical junctions with (a)10-aGNR, (b)12-aGNR, aGNR as left electrode and 6-zGNR as right electrode and the di-

(c)14-arylethene is in “closed” state (d)logT(e,V) plot for “open”

di-arylethene with 14-aGNR and z6GNR electrodes Dotted brownlines indicate the range of current integration around the Fermilevel Transmission peaks related to HOMO/LUMO are denoted

by yellow circles and yellow triangles 48

3.10 Mulliken charge analysis for the “closed” diarylethene molecule bedded in asymmetric GNRs junctions 49

em-3.11 Spatially resolved local density of states along the transport axis for

(a) 6-zGNR-“closed” diarylethene-10-aGNR (b) 6-zGNR-“closed”

diarylethene-14-aGNR junctions at different bias voltages The HOMO/LUMO

of diarylethene localized in the middle region and interface states

(ISs) localized at contacts can be clearly identified 50

4.1 Atomic structure of (n,m) gold SWNTs obtained by cylindrical

fold-ing of the 2D triangular lattice Basis vectors of the 2D lattice are

a1 and a2 (Reprinted with permission from Ref [133]) 56

4.2 Geometric structures of (5,3) and (5,5) Au nanotubes and a schematic

description of possible adsorbing sites for adsorption: Top, B1 (Bridge

site 1), B2 (Bridge site 2), Center 57

4.3 Adsorption geometries for CO adsorption on Au (5,3) at top (a),

B1 (b), and Au (5,5) at B1 (c) sites, oxygen adsorption on Au (5,3)

at center (d), B1 (e), and Au (5,5) at center (f) sites, respectively

The C, O, and Au atoms are depicted in grey, red, and yellow,

respectively 59

4.4 LDOS and orbitals of CO adsorbed on Au (5,3) at top (a), B1 (b)

sites and Au (5,5) at B1 (c) site The LDOS projected on the CO

molecule is shown in black and that projected on the gold atom

with the shortest distance from the C atom is colored yellow The

populations of CO orbitals are calculated through integrating over

the relevant peaks Included also are the vibrational frequencies of

stretching mode for different adsorption configurations Notice that

the frequency of free CO molecule is calculated as 2128 cm−1 62

4.5 Comparison of Au states after O atomic adhesion with those of thepristine (5,3) (a) and (5,5) (b) Au tubes For the adsorbed tubes,LDOS is projected onto Au atom with the shortest distance fromthe O atom 63

4.6 Quantum conductance spectrum for CO adsorbed Au (5,3)(a) and

Au (5,5) (b) The conductance spectra of pristine tubes (dashedlines) are also given for comparison 64

4.7 Quantum conductance spectrum for oxygen adsorbed Au (5,3) (a)and Au (5,5) (b) The conductance spectra of pristine tubes (dashedlines) are also given for comparison 65

4.8 Conductance as a function of energy for defective Au (5,3) tube withdefects arising from Au adhesion (a) and monovacancy (b) on thetube The relaxed defective structures are given as the insets, wherethe atoms around the defective site are highlighted by violet balls

It can be seen that the Au adatom distorts the tube differently atdifferent adsorption sites 66

4.9 Conductance as a function of energy for defective Au (5,5) tube withdefects arising from Au adhesion (blue line) and monovacancy (redline) on the tube The relaxed defective structures are given as theinsets, where the atoms around the defective site are highlighted byviolet balls 67

4.10 Supercells of CNT (9,0) (upper) and CNT (5,5) (bottom) employed

in calculations Strains are applied by elongating or shortening thelength of tubes along the tube axis (z axis) with two outermostlayers (shadowed area) fixed to their bulk structures without strain

In all calculations, the periodically replicated CNTs (in both x and

y directions) are separated by a vacumm region of 10 ˚A 70

4.11 Relation between work function (W) and potentials of CNT (5,5)under -1% compressive strain 71

4.12 Work functions of CNT (5,5) and CNT (9,0) Vs strain Tensilestrain is positive and compressive strain is negative For CNT (5,5),the work function changes monotonically when strain changes from-10 % to +10 % For CNT (9,0), when strain changes from -2% and4%, the work function behaves similar to that of CNT (5,5) 72

4.13 Electron DOS as a function of energy for CNT (9,0) at differentcompressive (a), and tensile (b) strains Dashed lines denote Fermienergies Note: The electrostatic potential in the middle of vaccum

is set to be 0.0 eV 74

4.14 A schematic description of different adsorbing sites (purple circles)

of K atom on CNT (9,0) (left) and CNT (5,5) (right): Bridge sites

B1, B2 ; Hollow site H, and top site T Binding energies for different

sites are calculated to be B1 : 1.58 eV, B2 : 1.62 eV, H : 1.73 eV, T : 1.59 eV for CNT (9,0), and B1 : 0.95 eV, B2 : 0.92 eV, H : 1.04 eV,

T : 0.92 eV for CNT (5,5),repectively. 76

4.15 Work function of potassium deposited CNT (9,0) and CNT (5,5) Vs.deposition density (x in KxC) For CNT (9,0), the work functionreaches its minimum value of 2.2 eV at the coating density of 5.56%(denoted as A in (a)), and the minimum work function of CNT (5,5)

is 1.98 eV occurring at the coating density of 6.25% (B in (a)) Theatomic structures of K-coated CNT (9,0) and (5,5) with minimumwork functions are shown in Fig 5 (b) ( A: upper, and B: lower) 77

4.16 Strain effects on adsorption energies of K@CNTs, and work tions of K adsorbed CNTs: (a) Adsorption energy of a single K atom

func-on CNT (9,0) and (5,5) as a functifunc-on of strain; (b) Strain dence of work functions of K coated CNT (9,0) as shown in Fig 5(b) (upper), and K coated CNT (5,5) (lower one in Fig 5 (b)) 78

depen-4.17 (a) Calculated average charge transfer per K atom to CNT (5,5) andCNT (9,0) at different strains When strain changes from -10% to10%, the charge transfer for two tubes monotonically increases (b)Isosurface of the differential charge density between isolated CNT(5,5), K atoms, and K-coated CNT (5,5) 79

5.1 Atomic structure of the CCA/NNO/CCA MTJ The models arebuilt by stacking CCA directly on NNO along the [001] crystalinedirection 84

5.2 LDOS for the majority (top panels) and minority (bottom panels)spin electrons projeted to the O, Co and Nb atoms at the Co-NbO2

interface and in bulk region, respectively The vertical dashed lineindicates the position of the Fermi level 87

5.3 Variation of the planar averaged SP along the interface normal rection of the CCA/NNO/CCA MTJ, at various values of appliedstrain The position of the Co-NbO2 interface plane is indicated bythe vertical dashed line The horizontal dashed line corresponds to100% SP in each case 89

di-5.4 In-plane wave vector k = (k x , k y) dependence of majority-spin(a) and minority-spin (b) transmissions at the Fermi level of theCCA/NNO/CCA MTJ in the parallel magnetization configurationwithout strain (c) TMR ratio as a function of strain 92

5.5 The differences between majority-spin transmissions at the Fermilevel in the parallel magnetization configuration in strained and

strain free CCA/NNO/CCA MTJ: (a) G ↑↑ (−4%)−G ↑↑ (0), (c) G ↑↑ (4%)−

G ↑↑(0) The transmission at zero strain is given in (b) The Fermisurfaces corresponding to the two folded bands in the Brillouin zone

of the orthorhombic Co2CrAl are shown in (d) and (e), respectively 93

Chapter 1

Introduction

In last decades, Si-based technology has witnessed a great success in tronics However, as the trend of miniaturization of the device sizes continues, newphenomena and problems that are absent in microelectronics occurs Thanks tothe development of nanotechnology, a variety of nanomaterials, such as nanowiresand nanotubes, have been successfully produced, which triggers the emergence ofnanoelectronics and provides new opportunities to achieve continuing performanceimprovement in post-Si technology Among all the produced nanomaterials, carbonbased nanomaterials such as carbon nanotubes (CNTs) and graphene are strongcandidates in replacing Si In addition, molecular electronics which utilizes the ver-satile characteristics of molecules may lead to new devices Building an electronicdevice on top of individual molecules is one of the ultimate goals in nanoelectronics.Recently, spintronics is a particularly promising technology, where the spin states

microelec-Chapter 1 Introduction

of carriers are utilized as an additional degree of freedom for information ing and storage Combination of technologies in spintronics and nanoelectronicscould lead to a new generation of devices with novel functionalities and superiorperformance

building blocks of nanoelectronics

Quasi 1D nanomaterials such as metallic nanowires and nanotubes are quite ing in nanoelectronics due to their high current density and conductivity.[1 6] Asthe dimension of materials reduces to nanoscale regime in which the mean free

promis-path of electron is comparable to the size of the materials, conductance (G) of the

metallic 1D nanomaterials where the electrons transport ballistically is quantized

(G = NG0, G0 = 2e2/h).[7] Conductance quantization has been observed in a riety of 1D Au, Pt, Cu, Ag nanowires.[1 4] More recently, helical single-wall goldnanotubes were successfully synthesized in experiment.[8] Owning to their helicalstructures, gold nanotubes have unique electronic and catalytic properties It waspredicted by theoretical study that chiral current flowing through gold tubes mayinduce strong magnetic field.[9, 10] For the metallic nanowires or nanotubes, ad-sorption of even a single molecule on the surface of the materials can drasticallychange the conductance.[11, 12] The effects of adsorption of atoms and molecules

va-on the surface of these quasi 1D nanomaterials are widely investigated to evaluatethe influences on potential nanoelectronics applications.[3, 13]

Chapter 1 Introduction

In addition, low-dimensional carbon-based nanomaterials, such as CNTs[14] andgraphene,[15, 16] have attracted great attentions for applications in nanoelectron-ics due to their unique properties Depending on chirality of the tube, CNTs can

be either metallic or semiconducting, and exhibit interesting physical properties cluding long ballistic transport length,[17] high thermal conductivity,[18] and highmechanical strength.[19] Single-wall CNTs have been considered as possible na-noelectronic components such as diodes and field-effect transistors (FET).[20–23]Since the first successful production of CNT-based FET in 1998,[23] single-wallCNTs have been extensively investigated as a channel material for replacement of

in-Si to enhance the mobility and integration scale of electronic devices The ability

of controlling the polarity of conduction carriers in CNT is highly important in

na-noelectronics applications Normally, CNT devices present p-type behavior due to

oxygen molecules adsorbed on their surfaces.[24] n-type conduction in CNT-based

FET can be achieved by doping alkali atoms, which involves a charge transfer fromthe alkali atoms to CNT.[25] In addition, annealing in vacuum[26] or contactingwith metallic electrode with a low work function such as Ca[27] and Sc[28] has also

been reported to be effective ways of producing n-type CNT devices.

Graphene is a planar network of carbon atoms connected by strong covalent C-C

bonds that exhibits linear energy-momentum (E -K ) relation in the band ture around Fermi energy Velocities of electrons and holes in graphene are ∼108

struc-cm/s and the mobilities are 15 000 cm2/Vs at room temperature,[15] which aremuch higher than those of conventionally used semiconducting materials Theseproperties make graphene a promising new material for applications in transistorsand integrated circuits However, the lack of a bandgap in graphene sheets hinders

Chapter 1 Introduction

high ON/OFF current ratios in electronic devices One way to create bandgaps

in graphene is to pattern graphene sheets into nanoribbons, which have attractedgreat interest due to their potential applications in nanoelectronics.[29, 30] Agraphene nanoribbon (GNR) can be either semiconducting or metallic depending

on its edge geometry Ribbons with zigzag edges (zGNRs) were shown to be lic, whereas the armchair edged ribbons (aGNRs) are semiconducting with energygaps inversely scaling with the ribbon width.[31] They can be obtained either bytailoring two-dimensional (2D) graphene or unzipping CNTs to 1D pattern.[32]However, perfect edges on nanoribbons are difficult to achieve Theoretical cal-culations suggest that edge roughness will have a large impact on their electronicproperties.[33,34] Besides the approach of making GNRs, other proposed methods

metal-of tuning the electronic structure metal-of graphene include applying external fields,[35]chemical adsorption,[36,37] exerting strain[38] and periodic potential,[39] or usingbilayer graphene.[40]

and molecular switch

1.2.1 Molecular diode

A diode or a rectifier, which allows an electric current to flow in one directionbut blocks it in the opposite direction, is an important component in electroniccircuits The concept of a molecular diode was firstly proposed by Aviram and

Chapter 1 Introduction

Rater (A-R).[41] This molecular diode consists of a system with a donor group

and an acceptor group which are separated by a σ-bonded segment The flow of

charges from cathode to anode can be described by a three-stage electron tunnelingprocess: cathode to acceptor, acceptor to donor, and donor to anode The key toobtain a large rectification ratio is to create a proper alignment of the acceptorand donor levels, through which tunneling in the forward bias direction is stronglyfavored

The A-R type of molecular diode was fabricated for the first time using Blodgett C16H33Q-3CNQ monolayer sandwiched between two planar Pt and Ag

Langmuir-electrodes, where the p-dodecyloxyphenyl group is the donor group, and the 3CNQ

moiety is the acceptor group.[42] Other experiment[43] using different electrodesconfirmed that the rectification observed in the above experiment[42] was due to themolecule itself rather than the metallic interface Rectification was also observed inself-assembled monolayers of block copolymers in scanning probe experiments.[44]While the above experiments were performed with a large number of molecules,single molecule diode has been demonstrated in a molecule consisting of two weaklycoupled conjugated units, using a mechanically controlled break-junction (MCBJ)method.[45] In this experiment, the two conjugated units in the molecule, with onebeing fluorized and the other one not, are different and this breaks the symmetry

of the molecular junction When sweeping the bias voltage, the energy levels ofboth units are shifted relative to each other, and different currents for differentbias polarities lead to the diode behavior

In addition to the Aviram and Rater’s approach, there are other proposals forcreation of molecular diodes based on different mechanisms, such as Coulomb

asym-of single-molecule based devices generally has a limit asym-of 100.[54] Although for somesingle-molecule rectifiers, theoretical studies based on semi-empirical methods give

high rectification ratio (>>100), more reliable first principles calculations for the same systems predicted a much lower ratio (<100).[55] Search for new mechanisms

of molecular junctions that can exceed the limit of rectification ratio, 100, is one

of the central issue of the field.[55]

1.2.2 Molecular switch

Single-molecule based switch holds great promise for the design of memory andlogic components in nanoelectronics Two approaches to realize molecular switch-ing have been proposed, including control of the orbital of the molecule throughelectric field[56] and control of the conformation of the molecule in response toexternal triggers.[57] For both approaches, the key is to translate the changes inmolecular orbital or molecular structure into changes in molecular conductivity to

in-to be an effective way in-to tune the performance of electron transport through themolecule (Fig 1.1).[56] For the latter approach, among various triggers, light is avery attractive external stimulus because of ease of addressability, fast responsetimes, and compatibility with a wide range of condensed phases Light-drivenswitching of the so-called photochromic molecules has been carried out by severalexperimental and theoretical groups.[57–59]

Photochromic molecules are compounds capable of undergoing a reversible phototransformation between two stable states, and have attracted remarkable inter-ests due to their potential applications in optoelectronic devices Among them,diarylethene is one of the most promising compounds due to its excellent thermalstability and high fatigue resistance and has been widely exploited to reversiblycontrol the conductance connected with gold nanoparticles.[60, 61] The key idea

Chapter 1 Introduction

Figure 1.2: Switching cycle of diarylethenes

underlying the diarylethene based switches is that two light convertible isomers

of the molecule, an “open” and a “closed” isomers (as shown in Fig 1.2), havedramatically different conductances when connected with metal leads Structuraldeformation between the “closed” and “open” states during photo transformation

leads to the reorganization of the π-conjugated backbone of the molecule, and

junc-tion based on the “closed” isomer with longer conjugajunc-tion path-length has largerconductance than that of the “open” isomer (Fig 1.2) Metal-diarylethene junc-tions have been extensively studied both theoretically and experimentally for theirapplications in molecular switches.[61–63]

To make an optic switch by photochromic molecules such as diarylethene, one lenge is related to immobilization of the molecule to external bulk surface.[64] Forexample, although switching between “open” and “closed” forms of the thiophene-based diarylethene is reversible in solution, it can only be switched from the

chal-“closed” to the “open” form once it is connected to gold via the Au-S bond.[62,65]The irreversibility is theoretically attributed to quenching of the excited states of

the “open” form associated with mixing with Au 3d orbitals Density functional

theory calculations[66, 67] revealed that the quenching observed may result fromthe alignment of the Fermi level of gold with the molecular frontier orbitals of the

“open” isomers The deep-lying highest occupied molecular orbital level of the

Chapter 1 Introduction

“open” isomer locates at a high 3d density of states of the metallic electrode, thus

facilitating electron transfer events, and thereby reducing the lifetime of the holecreated after excitation In contrast, the highest occupied molecular orbital of the

“closed” isomer is higher in energy and lies in a region of low density of states ofgold, hence ring opening can take place Although a simple solution to preservethe reversibility of the switch is to isolate the switching unit by non-conjugatedlinker like CH2 group,[67] however, the electron transport would then be substan-tially reduced and the ON/OFF ratio between the conductances of the “closed”and “open” forms would be lowered The use of carbon electrode like CNT orGNR is believed to be an effective way to preserve the reversibility due to lack of

M Julli`ere observed the effect of tunnel magnetoresistance (TMR) in a Fe/GeO/Co

Chapter 1 Introduction

magnetic tunneling junction (MTJ).[70] In 1988, A Fert and P A Gr¨unberg pendently discovered the giant magnetoresistance (GMR) in layered thin films offerromagnetic metal alternated to a non-magnetic metal.[71, 72] The discovery ofGMR stimulates tremendous interests in the field of spintronics and opens the door

inde-to a wealth of new scientific and technological possibilities To fabricate spintronicsdevices, a highly spin-polarized current is strongly desired Generally, there areseveral promising ways to obtain highly spin-polarized carriers

The first approach is to use a semiconducting or insulating barrier to selectivelyfilter carriers with one spin state from normal ferromagnetic metals such as Co or

Fe, as demonstrated in the Fe/MgO/Fe MTJ.[73] Considering the complex bandstructure of the barrier, different electronic states have different symmetries, whichresults in different tunneling probabilities for each spin direction and leads to spinpolarized current Therefore, the ferromagnetic electrode and the tunneling barrierplay important roles in obtaining a highly spin polarized current In addition,theoretical calculation has shown that interface formed between the electrode andbarrier can strongly influence the spin polarization(SP) and TMR of MTJ.[74]Recently, adoption of half metal as the spin source is widely investigated Half-metallic ferromagnets have a band gap at the Fermi energy (EF) for electronswith one spin direction, whereas they are metallic with respect to electrons withthe opposite spin direction (Fig 1.3) Therefore, a fully spin-polarized currentand a high spin injection efficiency are predicted for these compounds Some halfmetals have been theoretically predicted, including Fe3O4,[75] CrO2,[76] doubleperovskites,[77] zinc-blende-type CrAs[78] and Heusler alloys.[79]

Among all the half-metallic ferromagnets, Heusler alloys are promising materials for

Chapter 1 Introduction

spintronics applications, due to their high Curie temperatures and large magneticmoments per unit cell Unfortunately, although a full SP is predicted for bulkHeusler alloys, the measured SP is usually much lower Most of the Heusler alloyslose the high SP due to phase disorder and defects in bulk materials.[80] Moreimportantly, when a Heusler alloy is heterogeneously grown on another material,the charge-discontinuity related interface states can dramatically weaken the SP

at the interface and reduce the TMR ratio.[81] In addition, interface strain due tolattice mismatch may affect its SP Theoretical calculation has shown that straincan alter the width of the minority band gap and the position of the Fermi level inthe minority band gap.[82] It has been demonstrated that a 0.08% strain applied

to the NiMnSb half-Heusler alloy changes its magnetic anisotropy by 20%.[83] Asimilar strain-induced effect was observed in Co2MnGa.[84]

The second method is the use of spin filtering layers where a nonmagnetic electrode

is combined with a ferromagnetic or ferrimagnetic insulating tunnel barrier.[85] Inthe insulating magnetic layer, the conduction bands are spin polarized due toexchange effect, which creates two different barrier heights for spin-up and spin-down electrons from the nonmagnetic electrode Since the tunneling probabilityfor the carrier is inversely related to the barrier height, electrons with one spindirection can tunnel through the barrier much easier than electrons with the otherspin direction, which leads to a highly spin polarized current

In addition, the recently developed ability to manipulate electron spin in moleculesoffers a new route towards spintronics, and a new field of molecular spintronics thatcombines spintronics and molecular electronics is emerging.[86, 87] Among all themolecules, organic molecules are quite promising since they exhibit weak spin-orbit

Despite a great progress in nanotechnology such as in synthesizing nanomaterialsand fabricating nanoelectronics devices in recent years, understanding the under-lying mechanisms of observed phenomena in nanoscale is still a great challenge.This challenge originates from the quantum mechanical nature of the interactionsbetween atoms which can not be accurately treated with phenomenological or clas-sical method used in microelectronics The increase of complexity in nanoscale alsoleads to difficulties in explaining the experiments from an atomic-scale perspectivewhich is important in understanding the growth of nanomaterials, interface struc-ture, and measured properties of nanomaterials In addition, there are many issuesneeded to be clearly understood for fabricating high-performance nanoelectronicsand spintronics devices Among all the factors, chemical adsorption and strain are

Chapter 1 Introduction

critically important and their effects should be analyzed since they are inevitableduring fabrication or operation For CNTs, although chemical doping and strainhave been both widely investigated with respect to the electronic properties, theireffects on work function have less been explored Similarly, for Au nanotubes, de-tailed studies on the effects of chemical adsorption of molecules or atoms on theconductance fell short For spintronics devices, the strain induced effect on TMR

of MTJ is important from both technological side and physical side Structuraldeformations due to lattice mismatch of different materials in MTJs can stronglyalter the magnetic properties of the ferromagnet or the complex band structure ofthe semiconducting or insulating layer However, strain effect on spin polarizationand TMR of MTJ has not been systematically investigated

Motivated by the above issues, the aim of this thesis is to study physical properties

of various kinds of nanomaterials for applications in nanoelectronics and ics devices and to analyze new effects arising from variations such as strain andchemical dopings through first principles calculations within the framework of den-sity functional theory (DFT) The first-principles approach based on DFT has beenwidely adopted to study materials in both micro- and nanoscale In Chapter 2,basic principles of DFT and non-equilibrium Green’s function technique (NEGF)are presented In Chapter 3, a molecular switch and diode made from diarylethenemolecule is discussed Electronic structure and transport properties of a singlelight sensitive diarylethene molecule sandwiched between two GNRs were investi-gated In Chapter 4, factors that influence the properties of two types of nanotube(gold nanotube and CNT) are discussed For the gold nanotube, the effects of ad-sorbates (CO molecule and O atom) and defects on the electronic structures and

of CNT-based electronic devices In Chapter 5, electronic structure and TMR ofMTJ of Co2CrAl/NaNbO3/Co2CrAl are studied Variations of spin polarization(SP) and spin injection across the interface with strain are presented Finally,Chapter 6 presents the summary of this thesis.

Chapter 2

First-principles Methods

Since the 30s of last century, physicists have come to realize that, in principle,most of problems of materials can be explained by solving the time-dependentSchr¨odinger equation of the many-body system However, the complexity of the

macroscopic solid which comprises huge number of nucleus and electrons (∼1023)makes the solving of the equation intractable Although the Born-Oppenheimerapproximation[88] can reduce the problem to solve only the electrons moving in a

“frozen” field of nucleus, an accurate and affordable method of solving the tronic part of the equation is still a great challenge In the first part of thischapter, i will introduce the DFT which has been widely adopted to investigatethe electronic structure of many-body systems, in particular atoms, molecules, andcondensed phases The pseudopotential technique, that makes the DFT based cal-culations practical, is included in the second part The non-equilibrium Green’sfunction method which has been used to simulate the properties of open systems

elec-Chapter 2 First-principles Methods

is briefly described in the last part of the chapter

In principle, most problems of materials can be explained by solving Schr¨odingerequation of the many-body system comprised of electrons and nucleus However,lots of approximations have to be made to solve the problem Based on the Born-Oppenheimer approximation,[88] the Schr¨odinger equation of a many-body systemcomprised of nucleus and electrons can be simplified to only consider the movement

of electrons, while the nucleus are treated as fixed particles which generate a staticpotential Most of the properties of the material depend on solving the many-

electron problem The stationary Schr¨odinger equation for a system including N

is the Hamiltonian of the electronic system ˆT is the kinetic operator and ˆ V is the

external potential operator describing the Coulomb interaction between electronsand nucleus The ˆVee operator describes the electron-electron Coulomb interaction.The difficulty in solving the above equation arises from the electron-electron in-teraction In the Hartree and Hartree-Fock approximations, the electron-electron

Chapter 2 First-principles Methods

interaction is approximated by an effective potential, thus the many-electron teracting problem becomes a single-electron non-interacting problem which can beeasily solved

in-2.1.1 Hohenberg-Kohn theory and Kohn-Sham equation

In the original article in 1964,[89] Hohenberg and Kohn proved that the density

of electrons uniquely determines the external potential related to nuclei-electroninteraction up to a constant Since the potential determines all ground state prop-erties of the system, they suggested that the density can be used as the basicvariable of the problem The density functional theory is based on the followingtwo theorems:

Theorem 1: The external potential is uniquely determined by the electronic density

(ρ(r)), except for a trivial additive constant.

This theorem shows that the ground state electron density can be served as the

fundamental quantity instead of the wave function Since ρ(r) determines the

external potential and the number of electrons, it determines the electronic

Hamil-tonian and all the other ground state properties The ground state energy E is a

functional of the density, thus:

Chapter 2 First-principles Methods

The functional FHK[ρ] is the sum of kinetic and Coulomb energies and independent

of the external potential V (r).

Theorem 2: The true ground-state density ρ0 minimizes the energy functional, E[ρ], subject only to the conservation of the total number of electrons.

The above two theorems show that the ground state properties can be determinedthrough a variational method by varying the electron density However, there arestill several things which remain uncertain:

1) What is the form of this functional FHK[ρ]?

2) How to define the electron density for a many-body interacting system?

3) If the above two problems are solved, how to determine the ground state electrondensity through the variational method?

Kohn and Sham[90] have introduced the idea of mapping many-body interactingelectrons into non-interacting electrons The kinetic energy as well as potentialenergy functionals can be divided into two parts: one of which can be calcu-lated exactly under the assumption of non-interacting electrons (similar to the HFmethod[91,92]) and a correction term They suggested the following separation of

F [ρ] for any interacting many-particle system:

F [ρ] = T [ρ] + Vee[ρ]

= Ts[ρ] + J[ρ] + Exc[ρ] (2.4)

where T [ρ] and Vee[ρ] are the exact kinetic energy functional and electron-electron

Chapter 2 First-principles Methods

interacting potential for the N interacting electrons, respectively Ts[ρ] is the

non-interacting approximation to the kinetic energy, and

= VH(r) + Vxc(r) + V(r) (2.12)

Chapter 2 First-principles Methods

Moreover, since we are now dealing with the non-interacting cases, the equationfor the particle wave functions is just the Schr¨odinger equations:

which are the so-called Kohn-Sham equation Since the effective potential Veff(r)

requires the information of the electron density ρ(r) which in turn needs the Veff(r),

so the above equations need to be solved in a self-consistent manner

Finally, the total energy of the interacting system can be written as

The form of the exchange-correlation energy functional Exc[ρ], which depends on

a wave function or an electron density, is generally unknown The effect of theexchange and correlation on the electronic system can be vividly viewed from theexchange-correlation (xc) hole picture.[93] A xc hole around a given point r is given

Chapter 2 First-principles Methods

by

ρxc(r, r 0 ) = g(r 0 , r) − ρ(r 0) (2.16)

where g(r 0 , r) is the density at r 0 given that one electron is at r ρ(r 0) is the normal

average density without including the electron at r Thus ρxc(r, r 0) describes the

hole dug into the average density ρ(r 0) around the electron at r This hole isnormalized

Z

ρxc(r, r 0)dr0 = −1 (2.17)

which reflects a total screening of the electron at r due to the combined effect ofthe Pauli principle between spin parallel electrons and the Coulomb interactionbetween spin unparallel electrons, where the later can’t be treated in Hartree-Fockmethod

The difference among the DFT methods is the choice of the functional form ofexchange-correlation energy In electronic structure calculations, the exchange-correlation energy functional is often approximated by the local density approxi-mation (LDA)[94,95] or by the generalized-gradient approximation (GGA).[96,97]

The LDA is the most common and straightforward approximation to the

exchange-correlation energy functional Within the LDA, the Exc[ρ] is written as[94,95]

of carriers are utilized as an additional degree of freedom for information ing and storage Combination of technologies in spintronics and nanoelectronicscould lead to a new generation of. .. understanding the growth of nanomaterials, interface struc-ture, and measured properties of nanomaterials In addition, there are many issuesneeded to be clearly understood for fabricating high-performance... properties of two types of nanotube(gold nanotube and CNT) are discussed For the gold nanotube, the effects of ad-sorbates (CO molecule and O atom) and defects on the electronic structures and